In my experience you can get all the way to Nairobi on pretty easy roads so a decent all terrain tyre would do. The road up to the Ethiopian border can be hell if it rains. I went through here in a period of rare flooding and it was a nightmare. Mud tyres would be the thing to have. If you continue on up in to Ethiopia it will get much harder. The north of that country is mountains and mud. It is recommend for only tracked vehicles in some areas in rainy season.